Arthur McMahon first took up sport shooting around 1962 and was chosen to represent Ireland at the Olympics on two occasions, in 1968 at Mexico City and 1972 in München, competing in the open skeet event where he placed 47th and 53rd respectively. He also served as the captain of the Irish shooting team at München. McMahon was a prolific shooter and competed in many international tournaments all over the world, including at the world championships in the United States in 1969 and winning silver medals at skeet events in East Germany and Bologna, Italy. A lawyer by trade, he resided in Blessington, Wicklow.